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For any two vectors vecp and vecq, show ...

For any two vectors `vecp` and `vecq`, show that `|vecp.vecq| le|vecp||vecq|`.

Text Solution

Verified by Experts

This inequality holds trivially when either `vecp=veco" or " vecq=vec0`. So let us assume that `|vecp|ne0ne|vecp|`.
Then we have
`(|vecp.vecq|)/(|vecp||vecp|)=costhetale1`
`rArr " " |vecp||vecq|`
[This inequality is also known as Cauchy-Schwartz inequality]
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